Simplify the following expression: $ t = \dfrac{q + 9}{7} - \dfrac{4}{7} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{q + 9}{7} \times \dfrac{7}{7} = \dfrac{7q + 63}{49} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{4}{7} \times \dfrac{7}{7} = \dfrac{28}{49} $ Therefore $ t = \dfrac{7q + 63}{49} - \dfrac{28}{49} $ Now the expressions have the same denominator we can simply subtract the numerators: $t = \dfrac{7q + 63 - 28 }{49} $ Distribute the negative sign: $t = \dfrac{7q + 63 - 28}{49}$ $t = \dfrac{7q + 35}{49}$ Simplify the expression by dividing the numerator and denominator by 7: $t = \dfrac{q + 5}{7}$